The Italian was never tested by the wildcard Olaru, cruising to a 6-1 6-3 success on the clay in the Romanian capital.
Knapp was ruthless as she illustrated the depth in quality between herself and a player ranked 820 places below her, converting five breaks of serve to ensure progress in one hour and 14 minutes.
Joining Knapp in the next stage of the WTA International tournament is seventh seed Petra Cetkovska, who came through a much tougher task, overcoming Alexandra Cadantu 6-3 6-2.
Ranked at 97 in the world, Cadantu would have hoped to provide Cetkovska with more of a challenge, but an error-stricken performance in which she committed nine double faults allowed the Czech to earn an easy win.
The main surprise of the day came as Bulgarian qualifier Elitsa Kostova came from a set down to beat France's Alize Lim 3-6 6-4 7-5.
Kostova looked to be heading for defeat after losing the opening set, but rallied superbly to book a spot in the second round in two hours and 27 minutes.
But, while Lim fell at the first hurdle, there were no difficulties for Silvia Soler-Espinosa and Danka Kovinic, both of whom eased through in straight sets.
Spaniard Soler-Espinosa hammered Kazakhstani qualifier Sesil Karatantcheva 6-2 6-1 in just an hour and two minutes, and Montenegrin Kovinic saw off another qualifier, Anett Kontaveit of Estonia, 6-1 6-4.
Elsewhere in the draw, there were wins for Serbian Aleksandra Krunic and Katarzyna Piter.